{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D5WCXZ62PE5WKM6KWAQBSXQI7H","short_pith_number":"pith:D5WCXZ62","canonical_record":{"source":{"id":"1211.1435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-07T01:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"fdb8d76a1ef295af31f22a1292b8a45377a3077f2dad14b5574df164fbc97edf","abstract_canon_sha256":"25ab96393c080799e6e93eedb2dae8089d22425d39b5ee3edd5b0fbde25ee1cc"},"schema_version":"1.0"},"canonical_sha256":"1f6c2be7da793b6533cab020195e08f9f69548ee4486273bf42e98b5f67efba1","source":{"kind":"arxiv","id":"1211.1435","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1435","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1435v2","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1435","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"D5WCXZ62PE5W","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5WCXZ62PE5WKM6K","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5WCXZ62","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D5WCXZ62PE5WKM6KWAQBSXQI7H","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-07T01:00:21Z","cross_cats_sorted":[],"title_canon_sha256":"fdb8d76a1ef295af31f22a1292b8a45377a3077f2dad14b5574df164fbc97edf","abstract_canon_sha256":"25ab96393c080799e6e93eedb2dae8089d22425d39b5ee3edd5b0fbde25ee1cc"},"schema_version":"1.0"},"canonical_sha256":"1f6c2be7da793b6533cab020195e08f9f69548ee4486273bf42e98b5f67efba1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:58.453351Z","signature_b64":"bDd0pUqC3wQzDhHVomVHqO3ifl9K9znHEzbia6MSxpioWSLf8SJFP2H3dj6esVNjCojPWecc2orFBN85kVvrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f6c2be7da793b6533cab020195e08f9f69548ee4486273bf42e98b5f67efba1","last_reissued_at":"2026-05-18T02:41:58.452939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:58.452939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1435","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/uL/TaB31nmAeU9fzxtYshN04C4txEWFemxKb58OFEE8sbnkziiMG70Q5RrHl1D9DpDJ6aa0KHyb8uUPwY5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:56:54.349461Z"},"content_sha256":"ce856ce71db085bbaabff9da8a267450d032dda5c54a4e4a40df90df79c922d3","schema_version":"1.0","event_id":"sha256:ce856ce71db085bbaabff9da8a267450d032dda5c54a4e4a40df90df79c922d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D5WCXZ62PE5WKM6KWAQBSXQI7H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrew Chernih, Quoc Thong Le Gia","submitted_at":"2012-11-07T01:00:21Z","abstract_excerpt":"In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions with decreasing scaling factors. We use symmetric collocation and give sufficient conditions for convergence and stability analysis is also presented. Numerical experiments support the theoretical results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1435","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNslwrPad/g7Ep0cjRsqL9qbU437KmNDjykaEk5qp+s75eEzrqQMgVD8v8CAifMGz32x3dHvf0cGXqHLSrCkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:56:54.349807Z"},"content_sha256":"9cbc47613d2094e95183ddc7940de6f580a170425c3f3572dd07cfceed40123e","schema_version":"1.0","event_id":"sha256:9cbc47613d2094e95183ddc7940de6f580a170425c3f3572dd07cfceed40123e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/bundle.json","state_url":"https://pith.science/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T22:56:54Z","links":{"resolver":"https://pith.science/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H","bundle":"https://pith.science/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/bundle.json","state":"https://pith.science/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5WCXZ62PE5WKM6KWAQBSXQI7H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D5WCXZ62PE5WKM6KWAQBSXQI7H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"25ab96393c080799e6e93eedb2dae8089d22425d39b5ee3edd5b0fbde25ee1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-07T01:00:21Z","title_canon_sha256":"fdb8d76a1ef295af31f22a1292b8a45377a3077f2dad14b5574df164fbc97edf"},"schema_version":"1.0","source":{"id":"1211.1435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1435","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1435v2","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1435","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"D5WCXZ62PE5W","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5WCXZ62PE5WKM6K","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5WCXZ62","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:9cbc47613d2094e95183ddc7940de6f580a170425c3f3572dd07cfceed40123e","target":"graph","created_at":"2026-05-18T02:41:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions with decreasing scaling factors. We use symmetric collocation and give sufficient conditions for convergence and stability analysis is also presented. Numerical experiments support the theoretical results.","authors_text":"Andrew Chernih, Quoc Thong Le Gia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-07T01:00:21Z","title":"Multiscale methods with compactly supported radial basis functions for the Stokes problem on bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1435","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce856ce71db085bbaabff9da8a267450d032dda5c54a4e4a40df90df79c922d3","target":"record","created_at":"2026-05-18T02:41:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"25ab96393c080799e6e93eedb2dae8089d22425d39b5ee3edd5b0fbde25ee1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-07T01:00:21Z","title_canon_sha256":"fdb8d76a1ef295af31f22a1292b8a45377a3077f2dad14b5574df164fbc97edf"},"schema_version":"1.0","source":{"id":"1211.1435","kind":"arxiv","version":2}},"canonical_sha256":"1f6c2be7da793b6533cab020195e08f9f69548ee4486273bf42e98b5f67efba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f6c2be7da793b6533cab020195e08f9f69548ee4486273bf42e98b5f67efba1","first_computed_at":"2026-05-18T02:41:58.452939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:58.452939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bDd0pUqC3wQzDhHVomVHqO3ifl9K9znHEzbia6MSxpioWSLf8SJFP2H3dj6esVNjCojPWecc2orFBN85kVvrDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:58.453351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce856ce71db085bbaabff9da8a267450d032dda5c54a4e4a40df90df79c922d3","sha256:9cbc47613d2094e95183ddc7940de6f580a170425c3f3572dd07cfceed40123e"],"state_sha256":"c204945dc15cd553b12d4acefa37736b290f1088596d692dfafc4e6d69ab1481"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mcEkq9A33EL8sXAziQI4uihwnFHx5aFPjAYw69msvRlp17JDrppL1ltEKxsGh67ulgHae3rBZo1KDTtMyFfGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:56:54.351767Z","bundle_sha256":"72d870eb6fbd93211ba9736263e2cec8e2f533bb03a8c87c66677f945e39df6a"}}